Question

Consider the circular loop having current $i$ and with central point $O$. The magnetic field at the central point $O$ is

• A. $\frac{2{\mu }_{0}i}{3\pi R}$ acting downward
• B. $\frac{5{\mu }_{0}i}{12R}$ acting downward
• C. $\frac{6{\mu }_{0}i}{11R}$ acting downward
• D. $\frac{3{\mu }_{0}i}{7R}$ acting downward

Answer 1

The correct option is B $\frac{5{\mu }_{0}i}{12R}$ acting downward

Magnetic field at the center due to the inner loop of radius $R=\frac{3}{4}\times \frac{{\mu }_{0}I}{2R}$ downwards

Magnetic field at the center due to the outer loop of radius $3R=\frac{1}{4}\times \frac{{\mu }_{0}I}{2\left(3R\right)}$ downwards

Magnetic field at center due to the two straight wire segments is zero.

Hence net magnetic field at center of loop $=\frac{3{\mu }_{0}I}{8R}+\frac{{\mu }_{0}I}{24R}$ downwards $=\frac{5{\mu }_{0}I}{12R}$ downwards